Business Statistics for Contemporary Decision Making (6th Edition) PDF

 This online teaching and learning environment integrates the entire digital textbook with the most effective instructor and student resources WRÀWHYHU\OHDUQLQJVW\OH With WileyPLUS: ‡ Students achieve concept ‡ Instru...

 This online teaching and learning environment integrates the entire digital textbook with the most effective instructor and student resources WRÀWHYHU\OHDUQLQJVW\OH With WileyPLUS: ‡ Students achieve concept ‡ Instructors personalize and manage mastery in a rich, their course more effectively with structured environment assessment, assignments, grade that’s available 24/7 tracking, and more ‡ manage time better ‡study smarter ‡ save money From multiple study paths, to self-assessment, to a wealth of interactive visual and audio resources, WileyPLUS gives you everything you need to personalize the teaching and learning experience. » F i n d o u t h ow t o M A K E I T YO U R S » www.wileyplus.com  ALL THE HELP, RESOURCES, AND PERSONAL SUPPORT YOU AND YOUR STUDENTS NEED! 2-Minute Tutorials and all Student support from an Collaborate with your colleagues, of the resources you & your experienced student user find a mentor, attend virtual and live students need to get started Ask your local representative events, and view resources www.wileyplus.com/firstday for details! www.WhereFacultyConnect.com Pre-loaded, ready-to-use Technical Support 24/7 Your WileyPLUS assignments and presentations FAQs, online chat, Account Manager www.wiley.com/college/quickstart and phone support Training and implementation support www.wileyplus.com/support www.wileyplus.com/accountmanager MAKE IT YOURS!  6T H E D I T I O N Business Statistics For Contemporary Decision Making  6T H E D I T I O N Business Statistics For Contemporary Decision Making Ken Black University of Houston—Clear Lake John Wiley & Sons, Inc. Vice President & Publisher George Hoffman Acquisitions Editor Franny Kelly Assistant Editor Maria Guarascio Executive Marketing Manager Amy Scholz Editorial Assistant Emily McGee Production Manager Dorothy Sinclair Senior Production Editor Sandra Dumas Senior Designer Madelyn Lesure Executive Media Editor Allison Morris Photo Department Manager Hilary Newman Production Management Services Aptara Associate Media Editor Elena Santa Maria This book was typeset in 10/12 Minion at Aptara®, Inc. and printed and bound by R. R. Donnelley/ Jefferson City. The cover was printed by R. R. Donnelley/Jefferson City. The paper in this book was manufactured by a mill whose forest management programs include sustained yield harvesting of its timberlands. Sustained yield harvesting principles ensure that the number of trees cut each year does not exceed the amount of new growth. This book is printed on acid-free paper. ⬁ Copyright © 2010, 2008, 2006, 2004 by John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600. 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Black, Ken Business Statistics: For Contemporary Decision Making, Sixth Edition ISBN 13 978-0470-40901-5 ISBN 13 978-0470-55667-2 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 For Carolyn, Caycee, and Wendi  BRIEF CONTENTS UNIT I INTRODUCTION 1 Introduction to Statistics 2 2 Charts and Graphs 16 3 Descriptive Statistics 46 4 Probability 92 UNIT II DISTRIBUTIONS AND SAMPLING 5 Discrete Distributions 136 6 Continuous Distributions 178 7 Sampling and Sampling Distributions 216 UNIT III MAKING INFERENCES ABOUT POPULATION PARAMETERS 8 Statistical Inference: Estimation for Single Populations 250 9 Statistical Inference: Hypothesis Testing for Single Populations 288 10 Statistical Inferences About Two Populations 342 11 Analysis of Variance and Design of Experiments 402 UNIT IV REGRESSION ANALYSIS AND FORECASTING 12 Simple Regression Analysis and Correlation 464 13 Multiple Regression Analysis 516 14 Building Multiple Regression Models 546 15 Time-Series Forecasting and Index Numbers 588 UNIT V NONPARAMETRIC STATISTICS AND QUALITY 16 Analysis of Categorical Data 644 17 Nonparametric Statistics 670 18 Statistical Quality Control 720 APPENDICES A Tables 765 B Answers to Selected Odd-Numbered Quantitative Problems 805 GLOSSARY 815 INDEX 825 The following materials are available at www.wiley.com/college/black 19 Decision Analysis C19-2 Supplement 1 Summation Notation S1-1 Supplement 2 Derivation of Simple Regression Formulas for Slope and y Intercept S2-1 Supplement 3 Advanced Exponential Smoothing S3-1 viii  CONTENTS Preface xvii Key Terms 36 About the Author xxvii Supplementary Problems 36 Analyzing the Databases 40 UNIT I Case: Soap Companies Do Battle 40 INTRODUCTION Using the Computer 41 1 Introduction to Statistics 2 3 Descriptive Statistics 46 Decision Dilemma: Statistics Describe the State of Business in India’s Countryside 3 Decision Dilemma: Laundry Statistics 47 1.1 Statistics in Business 4 3.1 Measures of Central Tendency: Ungrouped Data 47 1.2 Basic Statistical Concepts 5 Mode 48 1.3 Data Measurement 7 Median 48 Nominal Level 7 Mean 49 Ordinal Level 8 Percentiles 51 Interval Level 8 Steps in Determining the Location of Ratio Level 9 a Percentile 51 Comparison of the Four Levels of Data 9 Quartiles 52 Statistical Analysis Using the Computer: Excel and Minitab 11 3.2 Measures of Variability: Ungrouped Data 55 Summary 12 Range 55 Key Terms 12 Interquartile Range 56 Supplementary Problems 12 Mean Absolute Deviation, Variance, and Analyzing the Databases 13 Standard Deviation 57 Case: DiGiorno Pizza: Introducing a Frozen Pizza to Mean Absolute Deviation 58 Compete with Carry-Out 15 Variance 59 Standard Deviation 60 2 Charts and Graphs 16 Meaning of Standard Deviation 60 Empirical Rule 60 Decision Dilemma: Energy Consumption Around the World 17 Chebyshev’s Theorem 62 Population Versus Sample Variance and 2.1 Frequency Distributions 18 Standard Deviation 63 Class Midpoint 18 Computational Formulas for Variance and Relative Frequency 18 Standard Deviation 64 Cumulative Frequency 19 z Scores 66 2.2 Quantitative Data Graphs 21 Coefficient of Variation 67 Histograms 21 3.3 Measures of Central Tendency and Using Histograms to Get an Initial Overview Variability: Grouped Data 70 of the Data 23 Measures of Central Tendency 70 Frequency Polygons 23 Mean 70 Ogives 24 Median 71 Dot Plots 25 Mode 72 Stem-and-Leaf Plots 25 Measures of Variability 72 2.3 Qualitative Data Graphs 27 3.4 Measures of Shape 77 Pie Charts 27 Skewness 77 Bar Graphs 28 Skewness and the Relationship of the Mean, Pareto Charts 30 Median, and Mode 77 2.4 Graphical Depiction of Two-Variable Coefficient of Skewness 77 Numerical Data: Scatter Plots 33 Kurtosis 78 Summary 36 Box-and-Whisker Plots 78 ix x Contents 3.5 Descriptive Statistics on the Computer 81 UNIT II Summary 83 DISTRIBUTIONS AND SAMPLING Key Terms 84 Formulas 84 5 Discrete Distributions 136 Supplementary Problems 85 Decision Dilemma: Life with a Cell Phone 137 Analyzing the Databases 89 5.1 Discrete Versus Continuous Distributions 138 Case: Coca-Cola Goes Small in Russia 89 5.2 Describing a Discrete Distribution 139 Using the Computer 91 Mean, Variance, and Standard Deviation of 4 Probability 92 Discrete Distributions 140 Mean or Expected Value 140 Decision Dilemma: Equity of the Sexes in the Variance and Standard Deviation of a Workplace 93 Discrete Distribution 140 4.1 Introduction to Probability 94 5.3 Binomial Distribution 143 4.2 Methods of Assigning Probabilities 94 Solving a Binomial Problem 144 Classical Method of Assigning Probabilities 94 Using the Binomial Table 147 Relative Frequency of Occurrence 95 Using the Computer to Produce a Binomial Distribution 148 Subjective Probability 96 Mean and Standard Deviation of a Binomial 4.3 Structure of Probability 96 Distribution 149 Experiment 96 Graphing Binomial Distributions 150 Event 96 5.4 Poisson Distribution 154 Elementary Events 96 Working Poisson Problems by Formula 156 Sample Space 97 Using the Poisson Tables 157 Unions and Intersections 97 Mean and Standard Deviation of a Poisson Mutually Exclusive Events 98 Distribution 158 Independent Events 98 Graphing Poisson Distributions 159 Collectively Exhaustive Events 99 Using the Computer to Generate Poisson Complementary Events 99 Distributions 159 Counting the Possibilities 99 Approximating Binomial Problems by the The mn Counting Rule 99 Poisson Distribution 160 Sampling from a Population with 5.5 Hypergeometric Distribution 164 Replacement 100 Using the Computer to Solve for Hypergeometric Combinations: Sampling from a Population Distribution Probabilities 166 Without Replacement 100 Summary 169 4.4 Marginal, Union, Joint, and Conditional Key Terms 169 Probabilities 101 Formulas 170 4.5 Addition Laws 103 Supplementary Problems 170 Probability Matrices 104 Analyzing the Databases 175 Complement of a Union 107 Case: Kodak Transitions Well into the Digital Special Law of Addition 108 Camera Market 175 4.6 Multiplication Laws 111 Using the Computer 176 General Law of Multiplication 111 Special Law of Multiplication 113 4.7 Conditional Probability 116 6 Continuous Distributions 178 Independent Events 119 Decision Dilemma: The Cost of Human Resources 179 4.8 Revision of Probabilities: Bayes’ Rule 123 6.1 The Uniform Distribution 179 Summary 128 Determining Probabilities in a Uniform Key Terms 128 Distribution 181 Formulas 129 Using the Computer to Solve for Uniform Supplementary Problems 129 Distribution Probabilities 183 Analyzing the Databases 132 6.2 Normal Distribution 184 Case: Colgate-Palmolive Makes a “Total” Effort 133 History of the Normal Distribution 185  Contents xi Probability Density Function of the Normal Analyzing the Databases 245 Distribution 185 Case: Shell Attempts to Return to Premiere Status 245 Standardized Normal Distribution 186 Using the Computer 246 Solving Normal Curve Problems 187 Using the Computer to Solve for Normal Distribution Probabilities 194 UNIT III 6.3 Using the Normal Curve to Approximate MAKING INFERENCES ABOUT Binomial Distribution Problems 196 POPULATION PARAMETERS Correcting for Continuity 198 6.4 Exponential Distribution 202 8 Statistical Inference: Estimation Probabilities of the Exponential for Single Populations 250 Distribution 203 Decision Dilemma: Compensation for Using the Computer to Determine Exponential Purchasing Managers 251 Distribution Probabilities 205 Summary 207 8.1 Estimating the Population Mean Using the Key Terms 208 z Statistic (␴ Known) 253 Finite Correction Factor 256 Formulas 208 Estimating the Population Mean Using the z Supplementary Problems 208 Statistic when the Sample Size Is Small 257 Analyzing the Databases 212 Using the Computer to Construct z Confidence Case: Mercedes Goes After Younger Intervals for the Mean 258 Buyers 212 8.2 Estimating the Population Mean Using the Using the Computer 213 t Statistic (␴ Unknown) 260 The t Distribution 261 7 Sampling and Sampling Robustness 261 Distributions 216 Characteristics of the t Distribution 261 Decision Dilemma: What Is the Attitude of Reading the t Distribution Table 261 Maquiladora Workers? 217 Confidence Intervals to Estimate the Population Mean Using the t Statistic 262 7.1 Sampling 217 Using the Computer to Construct t Confidence Reasons for Sampling 218 Intervals for the Mean 264 Reasons for Taking a Census 218 8.3 Estimating the Population Proportion 267 Frame 219 Using the Computer to Construct Confidence Random Versus Nonrandom Intervals of the Population Proportion 269 Sampling 219 8.4 Estimating the Population Variance 271 Random Sampling Techniques 220 8.5 Estimating Sample Size 275 Simple Random Sampling 220 Sample Size when Estimating ␮ 275 Stratified Random Sampling 221 Determining Sample Size when Estimating p 277 Systematic Sampling 222 Summary 280 Cluster (or Area) Sampling 223 Key Terms 280 Nonrandom Sampling 224 Convenience Sampling 224 Formulas 280 Judgment Sampling 225 Supplementary Problems 281 Quota Sampling 225 Analyzing the Databases 284 Snowball Sampling 226 Case: Thermatrix 284 Sampling Error 226 Using the Computer 285 Nonsampling Errors 226 9 Statistical Inference: Hypothesis 7.2 Sampling Distribution of ⴚ x 228 Testing for Single Populations 288 Sampling from a Finite Population 235 7.3 Sampling Distribution of p̂ 237 Decision Dilemma: Word-of-Mouth Business Referrals Summary 241 and Influentials 289 Key Terms 242 9.1 Introduction to Hypothesis Testing 290 Formulas 242 Types of Hypotheses 291 Supplementary Problems 242 Research Hypotheses 291 xii Contents Statistical Hypotheses 292 Difference in Two Population Means Using the Substantive Hypotheses 294 t Test 357 Using the HTAB System to Test Hypotheses 295 Confidence Intervals 360 Rejection and Nonrejection Regions 297 10.3 Statistical Inferences for Two Related Type I and Type II Errors 298 Populations 365 9.2 Testing Hypotheses About a Population Hypothesis Testing 365 Mean Using the z Statistic (␴ Known) 299 Using the Computer to Make Statistical Inferences About Two Related Populations 367 Testing the Mean with a Finite Population 301 Confidence Intervals 370 Using the p-Value to Test Hypotheses 302 Using the Critical Value Method to 10.4 Statistical Inferences About Two Population Test Hypotheses 303 Proportions, p1 ⫺ p2 375 Using the Computer to Test Hypotheses About a Hypothesis Testing 375 Population Mean Using the z Statistic 306 Confidence Intervals 379 9.3 Testing Hypotheses About a Using the Computer to Analyze the Difference Population Mean Using the t Statistic in Two Proportions 380 (␴ Unknown) 308 10.5 Testing Hypotheses About Two Population Using the Computer to Test Hypotheses About a Variances 382 Population Mean Using the t Test 312 Using the Computer to Test Hypotheses About 9.4 Testing Hypotheses About a Proportion 315 Two Population Variances 386 Using the Computer to Test Hypotheses About a Summary 391 Population Proportion 319 Key Terms 391 9.5 Testing Hypotheses About a Variance 321 Formulas 391 9.6 Solving for Type II Errors 324 Supplementary Problems 392 Some Observations About Type II Errors 329 Analyzing the Databases 397 Operating Characteristic and Power Curves 329 Case: Seitz Corporation: Producing Quality Gear-Driven and Effect of Increasing Sample Size on the Linear-Motion Products 397 Rejection Limits 331 Using the Computer 398 Summary 334 Key Terms 335 11 Analysis of Variance and Design of Experiments 402 Formulas 335 Supplementary Problems 335 Decision Dilemma: Job and Career Satisfaction of Foreign Analyzing the Databases 338 Self-Initiated Expatriates 403 Case: Frito-Lay Targets the Hispanic Market 339 11.1 Introduction to Design of Experiments 404 Using the Computer 340 11.2 The Completely Randomized Design (One-Way ANOVA) 406 10 Statistical Inferences About One-Way Analysis of Variance 407 Two Populations 342 Reading the F Distribution Table 411 Decision Dilemma: Online Shopping 343 Using the Computer for One-Way ANOVA 411 Comparison of F and t Values 412 10.1 Hypothesis Testing and Confidence Intervals About the Difference in Two Means Using the 11.3 Multiple Comparison Tests 418 z Statistic (Population Variances Known) 346 Tukey’s Honestly Significant Difference (HSD) Test: The Case of Equal Sample Sizes 418 Hypothesis Testing 347 Using the Computer to Do Multiple Confidence Intervals 350 Comparisons 420 Using the Computer to Test Hypotheses About Tukey-Kramer Procedure: The Case of Unequal the Difference in Two Population Means Sample Sizes 422 Using the z Test 352 10.2 Hypothesis Testing and Confidence Intervals 11.4 The Randomized Block Design 426 About the Difference in Two Means: Using the Computer to Analyze Randomized Block Designs 430 Independent Samples and Population Variances Unknown 355 11.5 A Factorial Design (Two-Way ANOVA) 436 Hypothesis Testing 355 Advantages of the Factorial Design 436 Using the Computer to Test Hypotheses and Factorial Designs with Two Treatments 437 Construct Confidence Intervals About the Applications 437  Contents xiii Statistically Testing the Factorial Design 438 Supplementary Problems 509 Interaction 439 Analyzing the Databases 513 Using a Computer to Do a Two-Way ANOVA 444 Case: Delta Wire Uses Training as a Weapon 513 Summary 453 Using the Computer 515 Key Terms 454 13 Multiple Regression Analysis 516 Formulas 454 Supplementary Problems 455 Decision Dilemma: Are You Going to Hate Your Analyzing the Databases 458 New Job? 517 Case: The Clarkson Company: A Division of Tyco 13.1 The Multiple Regression Model 518 International 459 Multiple Regression Model with Two Independent Using the Computer 460 Variables (First Order) 519 Determining the Multiple Regression Equation 520 A Multiple Regression Model 520 UNIT IV 13.2 Significance Tests of the Regression Model REGRESSION ANALYSIS AND and Its Coefficients 525 FORECASTING Testing the Overall Model 525 12 Simple Regression Analysis Significance Tests of the Regression Coefficients 527 and Correlation 464 13.3 Residuals, Standard Error of the Estimate, Decision Dilemma: Predicting International Hourly and R 2 530 Wages by the Price of a Big Mac 465 Residuals 530 12.1 Correlation 466 SSE and Standard Error of the Estimate 531 Coefficient of Multiple Determination (R 2) 532 12.2 Introduction to Simple Regression Analysis 469 Adjusted R2 533 12.3 Determining the Equation of the Regression Line 470 13.4 Interpreting Multiple Regression Computer Output 535 12.4 Residual Analysis 477 A Reexamination of the Multiple Using Residuals to Test the Assumptions of the Regression Output 535 Regression Model 479 Using the Computer for Residual Analysis 480 Summary 539 12.5 Standard Error of the Estimate 484 Key Terms 540 12.6 Coefficient of Determination 487 Formulas 540 Relationship Between r and r 2 489 Supplementary Problems 540 12.7 Hypothesis Tests for the Slope of the Analyzing the Databases 543 Regression Model and Testing the Overall Case: Starbucks Introduces Debit Card 543 Model 489 Using the Computer 544 Testing the Slope 489 Testing the Overall Model 493 14 Building Multiple Regression 12.8 Estimation 494 Models 546 Confidence Intervals to Estimate the Conditional Decision Dilemma: Determining Compensation Mean of y : ␮y | x 494 for CEOs 547 Prediction Intervals to Estimate a Single Value of y 495 14.1 Nonlinear Models: Mathematical 12.9 Using Regression to Develop a Forecasting Transformation 548 Trend Line 498 Polynomial Regression 548 Determining the Equation of the Trend Line 499 Tukey’s Ladder of Transformations 551 Forecasting Using the Equation of the Regression Models with Interaction 552 Trend Line 500 Model Transformation 554 Alternate Coding for Time Periods 501 14.2 Indicator (Dummy) Variables 560 12.10 Interpreting the Output 504 14.3 Model-Building: Search Procedures 566 Summary 508 Search Procedures 568 Key Terms 509 All Possible Regressions 568 Formulas 509 Stepwise Regression 568 xiv Contents Forward Selection 572 Summary 632 Backward Elimination 572 Key Terms 633 14.4 Multicollinearity 576 Formulas 633 Summary 580 Supplementary Problems 633 Key Terms 581 Analyzing the Databases 638 Formulas 581 Case: Debourgh Manufacturing Company 639 Supplementary Problems 581 Using the Computer 640 Analyzing the Databases 584 Case: Virginia Semiconductor 585 Using the Computer 586 UNIT V 15 Time-Series Forecasting and NONPARAMETRIC STATISTICS Index Numbers 588 AND QUALITY Decision Dilemma: Forecasting Air Pollution 589 16 Analysis of Categorical Data 644 15.1 Introduction to Forecasting 590 Decision Dilemma: Selecting Suppliers in the Electronics Time-Series Components 590 Industry 645 The Measurement of Forecasting Error 591 16.1 Chi-Square Goodness-of-Fit Test 646 Error 591 Testing a Population Proportion by Using the Mean Absolute Deviation (MAD) 591 Chi-Square Goodness-of-Fit Test as an Mean Square Error (MSE) 592 Alternative Technique to the z Test 652 15.2 Smoothing Techniques 594 16.2 Contingency Analysis: Chi-Square Test Naïve Forecasting Models 594 of Independence 656 Averaging Models 595 Summary 666 Simple Averages 595 Key Terms 666 Moving Averages 595 Formulas 666 Weighted Moving Averages 597 Supplementary Problems 666 Exponential Smoothing 599 Analyzing the Databases 668 15.3 Trend Analysis 604 Case: Foot Locker in the Shoe Mix 668 Linear Regression Trend Analysis 604 Using the Computer 669 Regression Trend Analysis Using Quadratic Models 606 Holt’s Two-Parameter Exponential Smoothing 17 Nonparametric Statistics 670 Method 609 15.4 Seasonal Effects 611 Decision Dilemma: How Is the Doughnut Decomposition 611 Business? 671 Finding Seasonal Effects with the Computer 614 17.1 Runs Test 673 Winters’ Three-Parameter Exponential Smoothing Small-Sample Runs Test 674 Method 614 Large-Sample Runs Test 675 15.5 Autocorrelation and Autoregression 616 17.2 Mann-Whitney U Test 678 Autocorrelation 616 Small-Sample Case 678 Ways to Overcome the Autocorrelation Large-Sample Case 680 Problem 619 17.3 Wilcoxon Matched-Pairs Signed Addition of Independent Variables 619 Rank Test 686 Transforming Variables 620 Small-Sample Case (n ⱕ 15) 686 Autoregression 620 Large-Sample Case (n ⬎ 15) 688 15.6 Index Numbers 623 17.4 Kruskal-Wallis Test 694 Simple Index Numbers 624 17.5 Friedman Test 699 Unweighted Aggregate Price Index Numbers 624 17.6 Spearman’s Rank Correlation 705 Weighted Aggregate Price Index Numbers 625 Summary 710 Laspeyres Price Index 626 Key Terms 711 Paasche Price Index 627 Formulas 711  Contents xv Supplementary Problems 711 APPENDICES Analyzing the Databases 716 A Tables 765 Case: Schwinn 717 B Answers to Selected Odd-Numbered Using the Computer 718 Quantitative Problems 805 GLOSSARY 815 18 Statistical Quality Control 720 INDEX 825 Decision Dilemma: Italy’s Piaggio Makes a Comeback 721 18.1 Introduction to Quality Control 722 The following materials are available at www.wiley.com/college/black What Is Quality Control? 722 Total Quality Management 723 19 Decision Analysis C19-2 Deming’s 14 Points 724 Decision Dilemma: Decision Making at the CEO Level C19-3 Quality Gurus 725 Six Sigma 725 19.1 The Decision Table and Decision Making Design for Six Sigma 727 Under Certainty C19-4 Lean Manufacturing 727 Decision Table C19-4 Some Important Quality Concepts 727 Decision Making Under Certainty C19-5 Benchmarking 728 19.2 Decision Making Under Uncertainty C19-6 Just-in-Time Inventory Systems 728 Maximax Criterion C19-6 Reengineering 729 Maximin Criterion C19-6 Failure Mode and Effects Analysis 730 Hurwicz Criterion C19-7 Poka-Yoke 731 Minimax Regret C19-9 Quality Circles and Six Sigma Teams 731 19.3 Decision Making Under Risk C19-14 18.2 Process Analysis 733 Decision Trees C19-14 Flowcharts 733 Expected Monetary Value (EMV) C19-14 Pareto Analysis 734 Expected Value of Perfect Information C19-18 Cause-and-Effect (Fishbone) Diagrams 735 Utility C19-19 Control Charts 736 19.4 Revising Probabilities in Light of Sample Check Sheets or Checklists 737 Information C19-22 Histogram 738 Expected Value of Sample Information C19-25 Scatter Chart or Scatter Diagram 738 Summary C19-32 18.3 Control Charts 739 Key Terms C19-33 Variation 740 Formula C19-33 Types of Control Charts 740 Supplementary Problems C19-33 ⫺ x Chart 740 Analyzing the Databases C19-36 R Charts 744 Case: Fletcher-Terry: On the Cutting Edge C19-36 p Charts 745 c Charts 748 SUPPLEMENTS Interpreting Control Charts 750 1 Summation Notation S1-1 Summary 756 2 Derivation of Simple Regression Key Terms 757 Formulas for Slope and y Intercept S2-1 Formulas 757 3 Advanced Exponential Smoothing S3-1 Exponential Smoothing with Trend Effects: Supplementary Problems 758 Holt’s Method S3-1 Analyzing the Databases 761 Exponential Smoothing with Both Trend and Case: Robotron-ELOTHERM 762 Seasonality: Winter’s Method S3-2 Using the Computer 763 Some Practice Problems S3-5 PREFACE The sixth edition of Business Statistics for Contemporary Decision Making continues the rich tradition of using clear and complete, student-friendly pedagogy to present and explain business statistics topics. With the sixth edition, the author and Wiley continue to expand the vast ancillary resources available through WileyPLUS with which to complement the text in helping instructors effectively deliver this subject matter and assisting students in their learning. The resources available to both the instructor and the student through WileyPLUS have greatly expanded since the fifth edition was launched; and because of this, an effort has been made in the sixth edition to more fully integrate the text with WileyPLUS. In the spirit of continuous quality improvement, several changes have been made in the text to help students construct their knowledge of the big picture of statistics, provide assistance as needed, and afford more opportunities to practice statistical skills. In the fifth edition, the 19 chapters were organized into four units to facilitate student under- standing of the bigger view of statistics. In the sixth edition, these same 19 chapters have been organized into five units so that chapters could be grouped into smaller clusters. The nonparametric and the analysis of categorical data chapters have been moved further toward the back of the text so that the regression chapters can be presented earlier. The decision trees that were introduced in the fifth edition to provide the student with a taxon- omy of inferential techniques have been improved and expanded in the sixth edition. Nonparametric inferential techniques have been separated from other inferential techniques and given their own decision tree. This has simplified the decision trees for parametric tech- niques and made the decision trees easier for students to decipher. Further integration of the text with WileyPLUS is addressed through icons that are used throughout the text to des- ignate to the reader that a WileyPLUS feature is available for assistance on a particular topic. The number of databases associated with the text has been expanded from seven to nine, and one of the fifth edition databases has been replaced, thereby bringing the total of new databases in the sixth edition to three. All of the features of the fifth edition have been retained, updated, and changed as needed to reflect today’s business world in the sixth edition. One Decision Dilemma has been replaced, and nine new Statistics in Business Today features have been added. In the sixth edition, as with the fifth edition, there are 17 high-quality video tutorials with the author explaining key difficult topics and demonstrating how to work problems from chal- lenging sections of the text. This edition is written and designed for a two-semester introductory undergraduate business statistics course or an MBA-level introductory course. In addition, with 19 chapters, the sixth edition lends itself nicely to adaptation for a one-semester introductory business sta- tistics course. The text is written with the assumption that the student has a college algebra mathematical background. No calculus is used in the presentation of material in the text. An underlying philosophical approach to the text is that every statistical tool presented in the book has some business application. While the text contains statistical rigor, it is written so that the student can readily see that the proper application of statistics in the business world goes hand-in-hand with good decision making. In this edition, statistics are presented as a means for converting data into useful information that can be used to assist the business decision maker in making more thoughtful, information-based decisions. Thus, the text presents business statistics as “value added” tools in the process of convert- ing data into useful information. CHANGES FOR THE SIXTH EDITION Units and Chapters The fifth edition presented 19 chapters organized into four units. The purpose of the unit organization was to locate chapters with similar topics together, thereby increasing the likelihood that students are better able to grasp the bigger picture of statistics. As an xvii xviii Preface example, in the fifth edition, Unit II was about distributions and sampling. In this unit of four chapters, the students were introduced to eight probability distributions and to methods of sampling that are used as the basis for techniques presented later in the text. In the sixth edition, the 18 chapters are organized into five units. The first two units of the sixth edition are the same as those used in the fifth edition. For several reasons, Unit III, Making Inferences About Population Parameters, which contained six chapters of statisti- cal techniques for estimating population parameters and testing population parameters in the fifth edition, has been reduced from six to four chapters in the sixth edition. This makes Unit III less formidable for students to digest, simplifies tree diagrams, and moves two chapters that are less likely to be covered in many courses to later in the text. In the sixth edition, Unit IV, now named Regression Analysis and Forecasting, consists of the same four chapters as it did in the fifth edition. In addition, these four chapters have been moved up two chapters in the sixth edition. Thus, the chapter on simple regression analysis, a chap- ter that is covered in most courses, is now Chapter 12 instead of Chapter 14. This organi- zation will make it easier for instructors to get to simple regression material without hav- ing to skip many chapters. Topical Changes Sections and topics from the fifth edition remain virtually unchanged in the sixth edition, with a few exceptions. Correlation analysis has been moved from Section 3.5 in the fifth edi- tion to Section 12.1 in the sixth edition. With this organization, the student begins the chap- ter (12) on simple regression analysis by studying scatter plots and correlation. Thus, the stu- dent is able to see visually what it means for variables to be related and to begin to imagine what it would be like to fit a line through the data. In addition, students are introduced to the r statistic as a forerunner of r 2, and they can see how the five-column analysis used to mechan- ically solve for r is similar to that used in solving for the equation of the regression line. In Chapter 2, Charts and Graphs, Section 2.2 of the fifth edition, has been expanded and reorganized into two sections, Quantitative Data Graphs and Qualitative Data Graphs. In addition, a treatment of dot plots has been added to Chapter 2 as an additional quanti- tative data graph. Dot plots are simple to construct and easy to understand and are espe- cially useful when analyzing small- and medium-size databases. Their importance in visu- ally depicting business data is growing. Upon request by text users, presentation of the median of grouped data has been added to Chapter 3, Descriptive Statistics. Acceptance sampling, the last section of Chapter 18 of the fifth edition, has been deleted in the sixth edition. Because acceptance sampling is based on inspection and is gen- erally only used to accept or reject a batch, it has limited usefulness in the present world of Six Sigma, lean manufacturing, and quality improvement. In place of acceptance sampling in the sixth edition, Chapter 18, Statistical Quality Control, additional information on quality gurus, quality movements, and quality concepts, has been added. Integration of Text and WileyPLUS WileyPLUS, with its rich resources, has been a powerful partner to this text in delivering and facilitating business statistics education for several years. Many instructors have dis- covered that WileyPLUS can greatly enhance the effectiveness of their business statistics course, and they use WileyPLUS hand-in-hand with the text. With this in mind, the sixth edition further integrates the text and WileyPLUS by using icons to represent such WileyPLUS features as interactive applets, videos by the author, demonstration problems, Decision Dilemma, Decision Dilemma Solved, flash cards, and databases showing exactly where each one corresponds to text topics. In this way, students are reminded in the text when there is a WileyPLUS feature available to augment their learning. Tree Diagram of Inferential Techniques To assist the student in sorting out the plethora of confidence intervals and hypothesis test- ing techniques presented in the text, tree diagrams are presented at the beginning of Unit III and Chapters 8, 9, 10, and 17. The tree diagram at the beginning of Unit III displays virtually  Preface xix all of the inferential techniques presented in Chapters 8–10 so that the student can construct a view of the “forest for the trees” and determine how each technique plugs into the whole. Then at the beginning of each of these three chapters, an additional tree diagram is presented to display the branch of the tree that applies to techniques in that particular chapter. Chapter 17 includes a tree diagram for just the nonparametric statistics presented in that chapter. In the fifth edition, all of these techniques were shown on one tree diagram; and because it was determined that this made the diagram less useful and perhaps overwhelming, in the sixth edition, the nonparametric branches are placed in a separate diagram. In determining which technique to use, there are several key questions that a student should consider. Listed here are some of the key questions (displayed in a box in the Unit III introduction) that delineate what students should ask themselves in determining the appropriate inferential technique for a particular analysis: Does the problem call for esti- mation (using a confidence interval) or testing (using a hypothesis test)? How many sam- ples are being analyzed? Are you analyzing means, proportions, or variances? If means are being analyzed, is (are) the variance(s) known or not? If means from two samples are being analyzed, are the samples independent or related? If three or more samples are being ana- lyzed, are there one or two independent variables and is there a blocking variable? Decision Dilemma and the Decision Dilemma Solved The popular Decision Dilemma feature included in previous editions of the text has been retained in the sixth edition along with the In Response feature, which has been renamed as Decision Dilemma Solved. The Decision Dilemmas are real business vignettes that open each chapter and set the tone for the chapter by presenting a business dilemma and asking a number of managerial or statistical questions, the solutions to which require the use of techniques presented in the chapter. The Decision Dilemma Solved feature discusses and answers the managerial and statistical questions posed in the Decision Dilemma using techniques from the chapter, thus bringing closure to the chapter. In the sixth edition, all decision dilemmas have been updated and revised. Solutions given in the Decision Dilemma Solved features have been revised for new data and for new versions of computer output. In addition, one new Decision Dilemma has been added in the sixth edition in Chapter 10. The title of this Decision Dilemma is “Online Shopping,” a current and timely topic in the business world. In this Decision Dilemma, the results of surveys by the Pew Internet/American Life Project of 2400 American adults and a Nielsen survey of over 26,000 Internet users across the globe are presented in addition to a Gallup household sur- vey of 1043 adults and a survey of 7000 people in Europe conducted by the European Interactive Advertising Association. Some of the findings of these studies include 875 mil- lion consumers around the world have shopped online, the market for online shopping has increased by 40% in the past 2 years, and European shoppers spend an average of €750 shopping online over a 6-month period. In the Decision Dilemma, presented at the open- ing of the chapter, students are asked to consider some managerial and statistical questions that are later answered in the Decision Dilemma Solved feature at the end of the chapter. An example of such as question, associated with this new Decision Dilemma is this: One study reported that the average amount spent by online American shoppers in the past 30 days is $123 at specialty stores and $121 at department stores. These figures are rela- tively close to each other and were derived from sample information. Suppose a researcher wants to test to determine if there is actually any significant difference in the average amount spent by online American shoppers in the past 30 days at specialty stores vs. department stores. How does she go about conducting such a test? Statistics in Business Today The sixth edition includes one or two Statistics in Business Today features in every chapter. This feature presents a real-life example of how the statistics presented in that chapter apply in the business world today. There are nine new Statistics in Business Today features in the sixth edition, which have been added for timeliness and relevance to today’s students, xx Preface and others have been revised and updated. The nine new Statistics in Business Today features are “Cellular Phone Use in Japan,” “Recycling Statistics,” “Business Travel,” “Newspaper Advertising Reading Habits of Canadians,” “Plastic Bags vs. Bringing Your Own in Japan,” “Teleworking Facts,” “Sampling Canadian Manufacturers,” “Canadian Grocery Shopping Statistics,” and “Rising Cost of Healthcare in the U.S.” As an example, from “Canadian Grocery Shopping Statistics,” Canadians take a mean of 37 stock-up trips per year, spending an average of 44 minutes in the store. They take a mean of 76 quick trips per year and average of 18 minutes in the store. On average, Canadians spend four times more money on a stock-up trip than on a quick trip. Twenty-three percent often buy items that are not on their list but catch their eye, 28% often go to a store to buy an item that is on sale, 24% often switch to another check out lane to get out faster, and 45% often bring their own bag. New Problems Every problem in the fifth edition has been examined for timeliness, appropriateness, and logic before inclusion in the sixth edition. Those that fell short were replaced or rewritten. While the total number of problems in the text is 950, a concerted effort has been made to include only problems that make a significant contribution to the learning process. Thirty new problems have been added to the sixth edition, replacing problems that have become less effective or relevant. Over one-third of the new problems are in Chapter 3, Descriptive Statistics, where it is especially important for the student to analyze up-to-date business sit- uations and data. All other problems in text have been examined for currency, and many problems have revised with updated data. All demonstration problems and example problems were thoroughly reviewed and edited for effectiveness. A demonstration problem is an extra example containing both a problem and its solution and is used as an additional pedagogical tool to supplement explanations and examples in the chapters. Virtually all example and demonstration prob- lems in the sixth edition are business oriented and contain the most current data available. As with the previous edition, problems are located at the end of most sections in the chapters. A significant number of additional problems are provided at the end of each chapter in the Supplementary Problems. The Supplementary Problems are “scrambled”— problems using the various techniques in the chapter are mixed—so that students can test themselves on their ability to discriminate and differentiate ideas and concepts. New Databases Associated with the sixth edition are nine databases, three of which are new to this edition. One new database is the 12-year Gasoline database, which includes monthly gasoline prices, the OPEC spot price each month, monthly U.S. finished motor gasoline production, and monthly U.S. natural gas well head prices over 12 years. A second new database is the Consumer Food database, which contains data on annual household income, non- mortgage household debt, geographic region, and location for 200 households. The third new database is a U.S. and International Stock Market database with 60 months of actual stock market data from the Dow Jones Industrial Average, the NASDAQ, Standard and Poor’s, Japan NIKKEI 225, Hong Kong Hang Seng, United Kingdom FTSE 100, and Mexico’s IPC. This new International Stock Market database replaced the old Stock Market database that was in the fifth edition. VIDEOTAPE TUTORIALS BY KEN BLACK An exciting feature of the sixth edition package that will impact the effectiveness of student learning in business statistics and significantly enhance the presentation of course material is the series of videotape tutorials by Ken Black. With the advent of online business statis- tics courses, increasingly large class sizes, and the number of commuter students who have  Preface xxi very limited access to educational resources on business statistics, it is often difficult for students to get the learning assistance that they need to bridge the gap between theory and application on their own. There are now 17 videotaped tutorial sessions on key difficult topics in business statistics delivered by Ken Black and available for all adopters on WileyPLUS. In addition, these tutorials can easily be uploaded for classroom usage to aug- ment lectures and enrich classroom presentations. Each session is around 9 minutes in length. The 17 tutorials are: 1. Chapter 3: Computing Variance and Standard Deviation 2. Chapter 3: Understanding and Using the Empirical Rule 3. Chapter 4: Constructing and Solving Probability Matrices 4. Chapter 4: Solving Probability Word Problems 5. Chapter 5: Solving Binomial Distribution Problems, Part I 6. Chapter 5: Solving Binomial Distribution Problems, Part II 7. Chapter 6: Solving Problems Using the Normal Curve 8. Chapter 8: Confidence Intervals 9. Chapter 8: Determining Which Inferential Technique to Use, Part I, Confidence Intervals 10. Chapter 9: Hypothesis Testing Using the z Statistic 11. Chapter 9: Establishing Hypotheses 12. Chapter 9: Understanding p-Values 13. Chapter 9: Type I and Type II Errors 14. Chapter 9: Two-Tailed Tests 15. Chapter 9: Determining Which Inferential Technique to Use, Part II, Hypothesis Tests 16. Chapter 12: Testing the Regression Model I—Predicted Values, Residuals, and Sum of Squares of Error 17. Chapter 12: Testing the Regression Model II—Standard Error of the Estimate and r 2 FEATURES AND BENEFITS Each chapter of the sixth edition contains sections called Learning Objectives, a Decision Dilemma, Demonstration Problems, Section Problems, Statistics in Business Today, Decision Dilemma Solved, Chapter Summary, Key Terms, Formulas, Ethical Considerations, Supplementary Problems, Analyzing the Databases, Case, Using the Computer, and Computer Output from both Excel 2007 and Minitab Release 15. Learning Objectives. Each chapter begins with a statement of the chapter’s main learning objectives. This statement gives the reader a list of key topics that will be discussed and the goals to be achieved from studying the chapter. Decision Dilemma. At the beginning of each chapter, a short case describes a real company or business situation in which managerial and statistical questions are raised. In most Decision Dilemmas, actual data are given and the student is asked to consider how the data can be analyzed to answer the questions. Demonstration Problems. Virtually every section of every chapter in the sixth edition contains demonstration problems. A demonstration problem contains both an example problem and its solution, and is used as an additional pedagogi- cal tool to supplement explanations and examples. Section Problems. There are over 950 problems in the text. Problems for practice are found at the end of almost every section of the text. Most problems utilize real data gathered from a plethora of sources. Included here are a few brief excerpts from some of the real-life problems in the text: “The Wall Street Journal reported that 40% of all workers say they would change jobs for ‘slightly higher pay.’ In xxii Preface addition, 88% of companies say that there is a shortage of qualified job candidates.” “In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all U.S. adults have invested in mutual funds.” “A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems.” “According to Padgett Business Services, 20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work. Twenty-five percent say the most important advice is to have good financing ready.” Statistics in Business Today. Every chapter in the sixth edition contains at least one Statistics in Business Today feature. These focus boxes contain an interesting application of how techniques of that particular chapter are used in the business world today. They are usually based on real companies, surveys, or published research. Decision Dilemma Solved. Situated at the end of the chapter, the Decision Dilemma Solved feature addresses the managerial and statistical questions raised in the Decision Dilemma. Data given in the Decision Dilemma are analyzed computationally and by computer using techniques presented in the chapter. Answers to the managerial and statistical questions raised in the Decision Dilemma are arrived at by applying chapter concepts, thus bringing closure to the chapter. Chapter Summary. Each chapter concludes with a summary of the important concepts, ideas, and techniques of the chapter. This feature can serve as a preview of the chapter as well as a chapter review. Key Terms. Important terms are bolded and their definitions italicized throughout the text as they are discussed. At the end of the chapter, a list of the key terms from the chapter is presented. In addition, these terms appear with their definitions in an end-of-book glossary. Formulas. Important formulas in the text are highlighted to make it easy for a reader to locate them. At the end of the chapter, most of the chapter’s formulas are listed together as a handy reference. Ethical Considerations. Each chapter contains an Ethical Considerations feature that is very timely, given the serious breach of ethics and lack of moral leadership of some business executives in recent years. With the abundance of statistical data and analysis, there is considerable potential for the misuse of statistics in business dealings. The important Ethical Considerations feature underscores this potential misuse by discussing such topics as lying with statistics, failing to meet statistical assumptions, and failing to include pertinent information for decision makers. Through this feature, instructors can begin to integrate the topic of ethics with applications of business statistics. Here are a few excerpts from Ethical Considerations features: “It is unprofessional and unethical to draw cause-and-effect conclusions just because two variables are correlated.” “The business researcher needs to conduct the experiment in an environment such that as many concomitant variables are controlled as possible. To the extent that this is not done, the researcher has an ethical responsibility to report that fact in the findings.” “The reader is warned that the value lambda is assumed to be constant in a Poisson distribution experiment. Business researchers may produce spurious results if the value of lambda is used throughout a study; but because the study is conducted during different time periods, the value of lambda is actually changing.” “In describing a body of data to an audience, it is best to use whatever statistical measures it takes to present a ‘full’ picture of the data. By limiting the descriptive measures used, the business researcher may give the audience only part of the picture and skew the way the receiver understands the data.” Supplementary Problems. At the end of each chapter is an extensive set of additional problems. The Supplementary Problems are divided into three groups: Calculating the Statistics, which are strictly computational problems; Testing Your Understanding, which are problems for application and understanding; and  Preface xxiii Interpreting the Output, which are problems that require the interpretation and analysis of software output. Analyzing the Databases. There are nine major databases located on the student companion Web site that accompanies the sixth edition. The end-of-chapter Analyzing the Databases section contains several questions/problems that require the application of techniques from the chapter to data in the variables of the databases. It is assumed that most of these questions/problems will be solved using a computer. Case. Each end-of-chapter case is based on a real company. These cases give the student an opportunity to use statistical concepts and techniques presented in the chapter to solve a business dilemma. Some cases feature very large companies— such as Shell Oil, Coca-Cola, or Colgate Palmolive. Others pertain to small businesses—such as Thermatrix, Delta Wire, or DeBourgh—that have overcome obstacles to survive and thrive. Most cases include raw data for analysis and questions that encourage the student to use several of the techniques presented in the chapter. In many cases, the student must analyze software output in order to reach conclusions or make decisions. Using the Computer. The Using the Computer section contains directions for producing the Excel 2007 and Minitab Release 15 software output presented in the chapter. It is assumed that students have a general understanding of a Microsoft Windows environment. Directions include specifics about menu bars, drop-down menus, and dialog boxes. Not every detail of every dialog box is discussed; the intent is to provide enough information for students to produce the same statistical output analyzed and discussed in the chapter. The sixth edition has a strong focus on both Excel and Minitab software packages. More than 250 Excel 2007 or Minitab Release 15 computer-generated outputs are displayed. WILEYPLUS WileyPLUS is a powerful online tool that provides instructors and students with an inte- grated suite of teaching and learning resources, including an online version of the text, in one easy-to-use Web site. To learn more about WileyPLUS, and view a demo, please visit www.wiley.com/college/WileyPLUS. WileyPLUS Tools for Instructors WileyPLUS enables you to: Assign automatically graded homework, practice, and quizzes from the end of chapter and test bank. Track your students’ progress in an instructor’s grade book. Access all teaching and learning resources, including an online version of the text, and student and instructor supplements, in one easy-to-use Web site. These include full color PowerPoint slides, teaching videos, case files, and answers and animations. Create class presentations using Wiley-provided resources, with the ability to customize and add your own materials. WileyPLUS Resources for Students Within WileyPLUS In WileyPLUS, students will find various helpful tools, such as an ebook, the student study manual, videos with tutorials by the author, applets, Decision Dilemma and Decision Dilemma Solved animations, learning activities, flash cards for key terms, demonstration problems, databases in both Excel and Minitab, case data in both Excel and Minitab, and problem data in both Excel and Minitab. xxiv Preface Ebook. The complete text is available on WileyPLUS with learning links to various features and tools to assist students in their learning. Videos. There are 17 videos of the author explaining concepts and demonstrating how to work problems for some of the more difficult topics. Applets. Statistical applets are available, affording students the opportunity to learn concepts by iteratively experimenting with various values of statistics and parameters and observing the outcomes. Learning Activities. There are numerous learning activities to help the student better understand concepts and key terms. These activities have been developed to make learning fun, enjoyable, and challenging. Data Sets. Virtually all problems in the text along with the case problems and the databases are available to students in both Excel and Minitab format. Animations. To aid students in understanding complex interactions, selected figures from the text that involve dynamic activity have been animated using Flash technology. Students can download these animated figures and run them to improve their understanding of dynamic processes. Flash Cards. Key terms will be available to students in a flash card format along with their definition. Student Study Guide. Complete answers to all odd-numbered questions. Demo Problems. Step-by-step solved problems for each chapter. ANCILLARY TEACHING AND LEARNING MATERIALS www.wiley.com/college/black Students’ Companion Site The student companion Web site contains: All databases in both Excel and Minitab formats for easy access and use. Excel and Minitab files of data from all text problems and all cases. Instructors and students now have the option of analyzing any of the data sets using the computer. Full and complete version of Chapter 19, Decision Analysis, in PDF format. This allows an instructor the option of covering the material in this chapter in the normal manner, while keeping the text manageable in size and length. A section on Advanced Exponential Smoothing Techniques (from Chapter 17), which offers the instructor an opportunity to delve deeper into exponential smoothing if so desired, and derivation of the slope and intercept formulas from Chapter 12. A tutorial on summation theory. Instructor’s Resource Kit All instructor ancillaries are provided on the Instructor Resource Site. Included in this con- venient format are: Instructor’s Manual. Prepared by Ken Black, this manual contains the worked out solutions to virtually all problems in the text. In addition, this manual contains chapter objectives, chapter outlines, chapter teaching strategies, and solutions to the cases. PowerPoint Presentation Slides. The presentation slides, prepared by Lloyd Jaisingh of Morehead State University, contain graphics to help instructors create stimulating lectures. The PowerPoint slides may be adapted using PowerPoint software to facilitate classroom use. Test Bank. Prepared by Ranga Ramasesh of Texas Christian University, the Test Bank includes multiple-choice questions for each chapter. The Test Bank is provided in Microsoft Word format.  Preface xxv ACKNOWLEDGMENTS John Wiley & Sons and I would like to thank the reviewers and advisors who cared enough and took the time to provide us with their excellent insights and advice, which was used to reshape and mold the test into the sixth edition. These colleagues include: Lihui Bai, Valparaiso University; Pam Boger, Ohio University; Parag Dhumal, Winona State University; Bruce Ketler, Grove City College; Peter Lenk, University of Michigan—Ann Arbor; Robert Montague, Southern Adventist University; Robert Patterson, Penn State University—Behrend; Victor Prybutok, University of North Texas; Nikolai Pulchritudoff, California State University—Los Angeles; Ahmad Saranjam, Northeastern University; Vijay Shah, West Virginia University; Daniel Shimshak, University of Massachusetts—Boston; Cheryl Staley, Lake Land College— Mattoon; Debbie Stiver, University of Nevada—Reno; Minghe Sun, University of Texas—San Antonio. As always, I wish to recognize my colleagues at the University of Houston–Clear Lake for their continued interest and support of this project. In particular, I want to thank William Staples, president; Carl Stockton, provost; and Ted Cummings, dean of the School of Business for their personal interest in the book and their administrative support. There are several people within the John Wiley & Sons publishing group whom I would like to thank for their invaluable assistance on this project. These include: Franny Kelly, Maria Guarascio, Allie Morris, Lisé Johnson, and Diane Mars. I want to express a special appreciation to my wife of 41 years, Carolyn, who is the love of my life and continues to provide both professional and personal support in my writing. Thanks also to my daughters, Wendi and Caycee, for their patience, love, and support. —Ken Black ABOUT THE AUTHOR Ken Black is currently professor of decision sciences in the School of Business at the University of Houston–Clear Lake. Born in Cambridge, Massachusetts, and raised in Missouri, he earned a bachelor’s degree in mathematics from Graceland University, a mas- ter’s degree in math education from the University of Texas at El Paso, a Ph.D. in business administration in management science, and a Ph.D. in educational research from the University of North Texas. Since joining the faculty of UHCL in 1979, Professor Black has taught all levels of statistics courses, forecasting, management science, market research, and production/ operations management. In 2005, he was awarded the President’s Distinguished Teaching Award for the university. He has published over 20 journal articles and 20 professional papers, as well as two textbooks: Business Statistics: An Introductory Course and Business Statistics for Contemporary Decision Making. Black has consulted for many different compa- nies, including Aetna, the city of Houston, NYLCare, AT&T, Johnson Space Center, Southwest Information Resources, Connect Corporation, and Eagle Engineering. Ken Black and his wife, Carolyn, have two daughters, Caycee and Wendi. His hobbies include playing the guitar, reading, traveling, and running. xxvii  UNIT I INTRODUCTION The study of business statistics is important, valuable, and interesting. However, because it involves a new language of terms, symbols, logic, and application of mathematics, it can be at times overwhelming. For many students, this text is their first and only introduction to business statistics, which instructors often teach as a “survey course.” That is, the student is presented with an overview of the subject, including a waterfront of tech- niques, concepts, and formulas. It can be overwhelming! One of the main difficulties in studying business statistics in this way is to be able to see “the forest for the trees,” that is, sorting out the myriad of topics so they make sense. With this in mind, the 18 chapters of this text have been organized into five units with each unit containing chapters that tend to present similar material. At the beginning of each unit, there is an intro- duction presenting the overlying themes to those chapters. Unit I is titled Introduction because the four chapters (1–4) contained therein “introduce” the study of business statistics. In Chapter 1, students will learn what statistics are, the concepts of descriptive and inferential sta- tistics, and levels of data measurement. In Chapter 2, students will see how raw data can be organized using various graphical and tabular techniques to facilitate their use in making better business decisions. Chapter 3 intro- duces some essential and basic statistics that will be used to both summa- rize data and as tools for techniques introduced later in the text. There will also be discussion of distribution shapes. In Chapter 4, the basic laws of probability are presented. The notion of probability underlies virtually every business statistics topic, distribution, and technique, thereby making it important to acquire an appreciation and understanding of probability. In Unit I, the first four chapters, we are developing “building blocks” that will enable students to understand and apply statistical concepts to ana- lyze data that can assist present and future business managers in making better decisions.  CHAPTER 1 Introduction to Statistics LEARNING OBJECTIVES The primary objective of Chapter 1 is to introduce you to the world of statistics, thereby enabling you to: 1. List quantitative and graphical examples of statistics within a business context 2. Define important statistical terms, including population, sample, and parameter, as they relate to descriptive and inferential statistics 3. Compare the four different levels of data: nominal, ordinal, interval, and ratio Keren Su/The Image Bank/Getty Images  Statistics Describe the State of Business in India’s Countryside India is the second largest country in done well in rural India, accounting for nearly one-half of all of the world, with more than a billion the country’s sales of televisions, fans, bicycles, bath soap, and people. Nearly other products. According to MART, a New Delhi–based three-quarters of research organization, rural India buys 46% of all soft drinks the people live in and 49% of motorcycles sold in India. In one year alone, the rural areas scat- market for Coca-Cola in rural India grew by 37%, accounting tered about the countryside in 6,000,000 villages. In fact, it may for 80% of new Coke drinkers in India. Because of such factors, be said that 1 in every 10 people in the world live in rural India. many U.S. and Indian firms, such as Microsoft, General Presently, the population in rural India can be described as poor Electric, Kellogg’s, Colgate-Palmolive, Hindustan Lever, Godrej, and semi-illiterate. With an annual per capita income of less Nirma Chemical Works, and Mahotra Marketing, have entered than $1 (U.S.) per day, rural India accounts for only about one- the rural Indian market with enthusiasm. Marketing to rural third of total national product sales. Less than 50% of house- customers often involves building categories by persuading holds in rural India have electricity, and many of the roads are them to try and adopt products that they may not have used not paved. The annual per capita consumption for toothpaste is before. Rural India is a huge, relatively untapped market for only 30 grams per person in rural India compared to 160 grams businesses. However, entering such a market is not without in urban India and 400 grams in the United States. risks and obstacles. The dilemma facing companies is whether However, in addition to the impressive size of the popula- to enter this marketplace and, if so, to what extent and how. tion, there are other compelling reasons for companies to mar- ket their goods and services to rural India. The market of rural India has been growing at five times the rate of the urban India Managerial and Statistical Questions market. There is increasing agricultural productivity, leading 1. Are the statistics presented in this report exact figures or to growth in disposable income, and there is a reduction in the estimates? gap between the tastes of urban and rural customers. The liter- 2. How and where could the researchers have gathered such acy level is increasing, and people are becoming more con- data? scious about their lifestyles and oppor- tunities for a better life. 3. In measuring the potential of the rural India marketplace, Nearly two-thirds of all middle- what other statistics could have been gathered? income households in India are in rural 4. What levels of data measurement are represented by data areas, with the number of middle- and on rural India? high- income households in rural India 5. How can managers use these and other statistics to make expected to grow from 80 million to better decisions about entering this marketplace? 111 million over the next three years. More than one-third of all rural house- Source: Adapted from Raja Ramachandran, “Understanding the Market holds now have a main source of Environment of India,” Business Horizons, January 2000; P. Balakrishna and B. Sidharth, “Selling in Rural India,” The Hindu Business Line—Internet income other than farming. Virtually Edition, February 16, 2004; Rohit Bansal and Srividya Easwaran, “Creative every home has a radio, almost 20% Marketing for Rural India,” research paper, http://www.indiainfoline.com; have a television, and more than 30% Alex Steffen, “Rural India Ain’t What It Used to Be,” WorldChanging; http://www.worldchanging.com/archives/001235.html; “Corporates Turn to have at least one bank account. Rural India for Growth,” BS Corporate Bureau in New Delhi, August 21, 2003, In the early 1990s, toothpaste con- http://www.rediff.com/money/2003/aug/21rural.htm; Rajesh Jain, “Tech Talk: sumption in rural India doubled, and The Discovery of India: Rural India,” June 20, 2003, http://www.emergic.org/ archives/indi/005721.php. “Marketing to Rural India: Making the Ends Meet,” the consumption of shampoo increased March 8, 2007, in India Knowledge@Wharton. http://knowledge.wharton. fourfold. Recently, other products have upenn.edu/india/article.cfm?articleid=4172 Every minute of the working day, decisions are made by businesses around the world that determine whether companies will be profitable and growing or whether they will stagnate and die. Most of these decisions are made with the assistance of information gathered about the marketplace, the economic and financial environment, the workforce, the competition, and other factors. Such information usually comes in the form of data or is accompanied by data. 3 4 Chapter 1 Introduction to Statistics Business statistics provides the tool through which such data are collected, analyzed, summa- rized, and presented to facilitate the decision-making process, and business statistics plays an important role in the ongoing saga of decision making within the dynamic world of business. 1.1 STATISTICS IN BUSINESS Virtually every area of business uses statistics in decision making. Here are some recent examples: According to a TNS Retail Forward ShopperScape survey, the average amount spent by a shopper on electronics in a three-month period is $629 at Circuit City, $504 at Best Buy, $246 at Wal-Mart, $172 at Target, and $120 at RadioShack. A survey of 1465 workers by Hotjobs reports that 55% of workers believe that the quality of their work is perceived the same when they work remotely as when they are physically in the office. A survey of 477 executives by the Association of Executive Search Consultants determined that 48% of men and 67% of women say they are more likely to negotiate for less travel compared with five years ago. A survey of 1007 adults by RBC Capital Markets showed that 37% of adults would be willing to drive 5 to 10 miles to save 20 cents on a gallon of gas. A Deloitte Retail “Green” survey of 1080 adults revealed that 54% agreed that plastic, non-compostable shopping bags should be banned. A recent Household Economic Survey by Statistic New Zealand determined that the average weekly household net expenditure in New Zealand was $956 and that households in the Wellington region averaged $120 weekly on recreation and culture. In addition, 75% of all households were satisfied or very satisfied with their material standard of living. The Experience’s Life After College survey of 320 recent college graduates showed that 58% moved back home after college. Thirty-two percent then remained at home for more than a year. You can see from these few examples that there is a wide variety of uses and applications of statistics in business. Note that in most of these examples, business researchers have con- ducted a study and provided us rich and interesting information. Nick M Do/iStock Exclusive/Getty Images, Inc. Comstock/Getty Images, Inc. William King/The Image Bank/ Getty Images, Inc.  1.2 Basic Statistical Concepts 5 In this text we will examine several types of graphs for depicting data as we study ways to arrange or structure data into forms that are both meaningful and useful to decision makers. We will learn about techniques for sampling from a population that allow studies of the business world to be conducted more inexpensively and in a more timely manner. We will explore various ways to forecast future values and examine techniques for predict- ing trends. This text also includes many statistical tools for testing hypotheses and for estimating population values. These and many other exciting statistics and statistical tech- niques await us on this journey through business statistics. Let us begin. 1.2 BASIC STATISTICAL CONCEPTS Business statistics, like many areas of study, has its own language. It is important to begin our study with an introduction of some basic concepts in order to understand and com- municate about the subject. We begin with a discussion of the word statistics. The word sta- tistics has many different meanings in our culture. Webster’s Third New International Dictionary gives a comprehensive definition of statistics as a science dealing with the collec- tion, analysis, interpretation, and presentation of numerical data. Viewed from this perspec- tive, statistics includes all the topics presented in this text. Photodisc/Getty Images, Inc. The study of statistics can be organized in a variety of ways. One of the main ways is to subdivide statistics into two branches: descriptive statistics and inferential statistics. To understand the difference between descriptive and inferential statistics, definitions of popula- tion and sample are helpful. Webster’s Third New International Dictionary defines popula- tion as a collection